Information
Former
2008/2009
Natural Sciences  Medicine  Mathematics
Abstract
The research program will focus on the mathematical discipline nonlinear partial differential equation. Differential equations have their origin in the quest to describe nature by mathematics, and these equations are perfect tools to describe physical phenomena that vary in space and time. In fact, all the fundamental laws of nature are given by differential equations (Newton’s law describes gravitation, Maxwell’s equations describe electromagnetism, Navier–Stokes’ equations describe fluid flow, etc). Thus they model a wide variety of phenomena, and have been extensively studied by mathematicians, physicists, engineers, and others. Differential equations constitute a core mathematical discipline, cf. the Abel Prize 2005. However, several key questions have not been answered, or only been partly answered. Central issues are: • Do the equations have a solution? It is still not known if the equations that describe the flow of air around an airplane have a solution. • Given that the equation has a solution, is it unique? For flow of oil in petroleum reservoirs the equations give several possible distinct values for the saturation at the same point in space. • Is the solution stable? Will a small change in one place in space have dramatic consequences in a completely different location (“the butterfly effect"). • If the equation has a unique and stable solution, how can one determine the solution? Given the measured weather data for today, how can one predict the weather for tomorrow? Variations of these questions for carefully selected nonlinear partial differential equations constitute the focus for the research program, in particular the interplay between theoretical results (mathematical properties of the solution) and numerical computations (how to compute the solution). Differential equations have been an intensive research area in mathematics in Norway the last two decades, and there are now strong research groups in Oslo, Trondheim, and Bergen. The research program will both benefit from the strong national activities and further strengthen it. Furthermore, applications to other areas of science will have impact there. The generic nature of mathematics means that the methods and techniques of this program can be applied to several seemingly distinct areas. We will focus on four applications, namely flow in porous media (e.g., flow of oil in a petroleum reservoir), mixtures of solids and fluids (e.g., sedimentation), gas dynamics (e.g., flow of gas around obstacles), water waves (e.g., breaking of waves).
Fellows

Amadori, DeboraDr. University of L'Aquila

Andreianov, Boris AndreianovDr. University of FrancheComté

Brenier, Yann University of Nice

Bressan, AlbertoProfessor Pennsylvania State University

Carrillo de la Plata, Jose AntonioProfessor Catalan Institution for Research and Advanced Studies (ICREA)

Chen, GuiQiang G.Professor University of Oxford

Coclite, Giuseppe MariaAssistant Professor University of Bari

Feireisl, EduardProfessor Institute of Mathematics of the Czech Academy of Sciences

Frid, HermanoProfessor Instituto de Matemática Pura e Aplicada (IMPA)

Gesztesy, FritzProfessor University of Missouri

HancheOlsen, HaraldAssociate Professor Norwegian University of Science and Technology (NTNU)

Jakobsen, Espen RobstadAssociate Professor Norwegian University of Science and Technology (NTNU)

Jenssen, KristianAssociate Professor Pennsylvania State University

Kalisch, HenrikAssociate Professor University of Bergen (UiB)

Karper, Trygve KlovningResearch Fellow Norwegian University of Science and Technology (NTNU)

Klainerman, SergiuProfessor Princeton University

Kwon, YoungSamDr. University of Maryland

LeFloch, Philippe GerardProfessor Pierre and Marie Curie University

Lindqvist, Lars PeterProfessor Norwegian University of Science and Technology (NTNU)

Liu, HailiangProfessor Iowa State University

Panov, Evgeniy Yuz'evichProfessor Novgorod State University

Raynaud, Xavier Marcel University of Oslo (UiO)

Risebro, Nils HenrikProfessor University of Oslo (UiO)

Rohde, ChristianProfessor University of Stuttgart

Sande, Hilde Norwegian University of Science and Technology (NTNU)

Selberg, SigmundAssociate Professor Norwegian University of Science and Technology (NTNU)

Serre, DenisProfessor ENS de Lyon

Shen, WenAssistant Professor Pennsylvania State University

Tadmor, EitanProfessor University of Maryland

Teschl, GeraldProfessor University of Vienna

Towers, John DavidProfessor Mira Costa College

Trivisa, KonstantinaProfessor University of Maryland

Zhaoyang, YinProfessor Zhongshan University
Previous events

26 May  27 May 2009(all day)Turrent Room, CAS, Oslo Turrent Room, CAS, Oslo

20 Aug  22 Aug 2008(all day)Turrent Room, CAS, Oslo Turrent Room, CAS, Oslo